Question

Heights of men in the United States are approximately normally distributed

with a mean of 70 inches and a standard deviation of 2.5 inches.
Part A: What is the probability that a randomly selected man will be taller than 75 inches?

Part B: According to our information, is 75 unusually tall for a man?

Answer 1

Part A: 2.5%

B: Yes, it is unusual because a height of 75 has a probability less than 5%

Explanation:

I did the thing

Answer 2

a. P(X>75)=0.02275

b. Yes

Explanation:

Given that the mean is 70 inches and the standard deviation is 2.5 inches.

-the probability that a random selection has a height greater than 75 inches is calculated as:

`P(X>75)\\\# compute\ z-score\\z=(\bar x-\mu)/(\sigma)\\\\z=(75-70)/(2.5)\\\\=2.00\\\\\therefore P(X>75)=1-P(X<75)\\\\=1-0.97725\\\\=0.02275`

Hence, the probability of a random being taller than 75 inches is 0.02275

b. Based on the above information, 75 inches is unusually tall since it has a deviation of 2.5 inches more than the standard deviation.